Obama stepped off Air Force One at Stockholm's Arlanda Airport fresh from efforts in Washington to secure bipartisan support for military action to punish President Bashar al-Assad for an alleged chemical weapons attack on a Damascus suburb last month.
Obama's trip will also take him to the G20 summit in Russia's Saint Petersburg, where White House officials said he would hold meetings with the president of France, the main foreign backer of US strikes on Syria, as well as the leaders of China and Japan.
"We would expect the two presidents to have an opportunity to speak on the margins of the various meetings of the G20," he said.
Putin today appeared to soften his stance towards the West over Syria, saying Russia did not exclude agreeing to US-led strikes on the war-torn country if it was proven beyond doubt that Assad's regime had carried out the deadly August 21 chemical attack.
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If there was clear proof of what weapons were used and who used them, Russia "will be ready to act in the most decisive and serious way," Putin told state-run Channel One television in an interview ahead of this week's G20 summit.
Even so, winning over the European nations will be an uphill struggle, as the British parliament demonstrated last week by voting against any strikes on the Syrian regime.
Sweden today also struck a cautious note.
"We need to come up with a forceful response," Swedish Foreign Minister Carl Bildt told local television. "We hope that the (UN) Security Council can agree on this."
Late last week, Swedish Prime Minister Fredrik Reinfeldt said he opposed "military solutions of a conflict which in my opinion should be resolved through political and diplomatic efforts."
"The world has noticed that our countries are dynamic economies that are doing relatively well despite the state of the global economy," he said.
Underlining the Nordic theme, Obama will have dinner today with the prime ministers of Norway, Denmark and Iceland as well as the president of Finland -- but even here, controversy could arise.